1. Field of the Invention
The present invention is directed to a gradient coil system for use in a nuclear magnetic resonance tomography apparatus, the gradient coil system having a symmetry plane in the x-y plane of a rectangular x-y-z coordinate system, with the z-axis proceeding in the direction of the fundamental magnetic field B.sub.Z.
2. Description of the Prior Art
In nuclear magnetic resonance tomography devices (also referred to as magnetic resonance imaging devices), it is known to use a saddle coil arrangement to generate an x-gradient field and to use a saddle coil arrangement to generate a y-gradient field, with respect to a fundamental magnetic field B.sub.Z. These saddle coil arrangements each contain four main coils, which are composed of saddle coils having divided inner arcs (split arc saddle coils) arranged on cylindrical generated surfaces. The main coils each consist of two elementary saddle coils, one inside the other. Each elementary saddle coil contains a front arc facing toward the x-y plane having a distance Z from the x-y plane, and a rear arc having a distance H from the x-y plane. The arcs are connected to each other by straight conductors proceeding in the z-direction. The position of these conductors is defined by an angle .phi. in the x-y plane. The straight conductors of the two elementary saddle coils are disposed approximately against each other. The rear arcs of the two elementary saddle coils are also disposed approximately against each other. Each elementary saddle coil has a predetermined amperage.
The nuclear magnetic resonance imaging device in which such a gradient coil system is used contains a fundamental field magnet system which aligns the nuclear spins in an examination subject, and also contains a RF system for exciting nuclear spins in the examination subject, and for acquiring the signals emitted by the excited spinning nuclei. The gradient fields generated by the gradient coil system are required for selecting a slice of the examination subject which is to be imaged, and for the spatial allocation of the signals in the slice. The gradient coil system contains gradient coils which generate a magnetic field proceeding in the direction of the fundamental field, changing linearly in this direction. Further gradient coils generate respective magnetic fields proceeding in the direction of the fundamental field which respectively change in two directions perpendicular to the direction of the fundamental field. By selectively operating these gradient coils, the phase of the signal induced in the RF system following the generation of the fundamental field is influenced dependent on the distribution of nuclear spins in the examination region. It is thus possible to generate an image of a slice plane of the examination subject based on the distribution of nuclear spins.
In addition to the fundamental field B=B.sub.0 .multidot.e.sub.z and an RF field B.sub.x, y, the gradient fields, which can be switched independently of each other, are required for generating a nuclear magnetic resonance image. These gradient fields are optimally linear gradient fields of the form: ##EQU1## The y-gradient field is difficult to produce because it is not dynamically balanced. The x-gradient field is generated by a coil system which is identical to the y-gradient coil system, but is rotated by 90.degree. about the z-axis. The effective z-component of the y-gradient field can best be represented by a series expansion according to spherical functions: ##EQU2## The specific symmetry only permits uneven indices and sineterms. In the above expansion, n is the degree of the Legendre polynomial expansion, m is the order of the Legendre polynomial expansion, r=(x.sup.2 +y.sup.2 +z.sup.2).sup.1/2, .phi. is the angle of the incident point relative to the x-axis, .upsilon. is the angle of the incident point relative to the z-axis, R is the radius of the imaging region, G.sub.y is the gradient strength, for example about 1 to 10 mT/m, P.sub.n.sup.M is the associated normalized Legendre polynomial expansion, and C(n,m) is the development coefficient, which equals the relative amplitudes of the field contribution of the type (n,m).
The normalizing of the Legendre polynomial expansion P.sub.n.sup.M is selected so that it can assume maximum values of about 1. The development coefficients C(n,m) then approximately represent the maximum value for points on a spherical surface having the radius R.
An ideal G.sub.Y coil system would only provide a coefficient C(1,1)=1.1545. Because the space relationships in a fundamental field magnet for nuclear magnetic resonance tomography are extremely tight, the gradient coils are generally constructed on cylindrical carrier members having a finite length. Higher noise terms C(n,m), with n&gt;1, and m&gt;1 arise as a result. The values having low n and m are particularly disturbing because they only decrease toward the center with the n.sup.th power of r. Disturbances having a high degree of n are more acceptable because they only take effect at the edge of the useful volume. A design of the gradient coils is thus needed wherein many development coefficients C (n,m) are zero given a constant C(1,1).
A known nuclear magnetic resonance tomography apparatus contains a system of gradient coils which simulates a hollow cylinder having the radius .pi. and having a cylinder axis proceeding in the z-direction of a rectangular x-y-z coordinate system which has its origin in the center of an imaging region. The magnetic field B.sub.Z of a fundamental field magnet also proceeds in this direction. At least two annular individual coils, symmetrically arranged relative to the x-y plane and traversed by current in opposite directions, are provided for generating a z-gradient which is at least approximately constant in the imaging region. The gradient coil system also includes at least one set of pairs of saddle-shaped individual coils arranged substantially symmetrically relative to the symmetry plane, which generate a substantially constant x-gradient ##EQU3## and a corresponding y-gradient ##EQU4## in the imaging region. These saddle coils each contain straight coil portions proceeding in the z-direction as well as coil portions proceeding as azimuthally relative to the z-axis in the circumferential direction of the cylinder. The directions of current conduction are the same in those coil portions of the two elementary saddle coils which neighbor one another. The directions of current conduction, however, are the same in the corresponding arc-shaped coil portions of the other coil pair which are symmetrically arranged relative to the symmetry plane. The coil arcs are arranged at predetermined distances from the symmetry plane, and the coupling in the coil arcs becomes higher with increasing distance from the symmetry plane. Significant noise terms C are eliminated by this splitting of those coils which are immediately adjacent the symmetry plane (split arc saddle coils). Such a coil system is described in U.S. Pat. No. 4,486,711.